Pith Number

pith:WL4IPTTP

pith:2019:WL4IPTTPYX7MVG6COKXDFF4DFU

not attested not anchored not stored refs pending

Double variational principle for mean dimension

Elon Lindenstrauss, Masaki Tsukamoto

arxiv:1901.05623 v1 · 2019-01-17 · math.DS · cs.IT · math.IT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WL4IPTTPYX7MVG6COKXDFF4DFU}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-17T23:56:06.611019Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2f887ce6fc5feca9bc272ae3297832d12e4d62602c53520dee1719bfa21f3e5

Aliases

arxiv: 1901.05623 · arxiv_version: 1901.05623v1 · doi: 10.48550/arxiv.1901.05623 · pith_short_12: WL4IPTTPYX7M · pith_short_16: WL4IPTTPYX7MVG6C · pith_short_8: WL4IPTTP

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WL4IPTTPYX7MVG6COKXDFF4DFU \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: b2f887ce6fc5feca9bc272ae3297832d12e4d62602c53520dee1719bfa21f3e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "747f3acfbc9d3f8d24b9954b5e6afb1f5e65e0ee7864a1e6f8429148cc51890f",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2019-01-17T05:24:48Z",
    "title_canon_sha256": "6e67b2673def4aa8c1c83655a7af6fa5a6571a8c25afb13ae843199a71e33691"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.05623",
    "kind": "arxiv",
    "version": 1
  }
}